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The A+LS Mathematics curriculum is a comprehensive, completely integrated curriculum for grade levels 1-12. A sequence of 18 titles provides an extensive, integrated solution that is fully correlated to major mastery standards and leading, adopted textbooks.
In addition to a complete mathematical curriculum that is appropriate at each grade level, each title contains exercises that require the student to choose operations and develop strategies to solve problems. Students learn to use common sense, mental math, estimation, and other methods to solve problems and check answers for reasonableness.
The Mathematics titles develop knowledge of mathematics skills and their use in practical situations by utilizing a four-step approach: Study, Practice, Test, and Essay modules are used to define the instructional environment. The Study module provides a text- and graphics-based delivery of material that is reinforced by pictures and diagrams supported by a wealth of content. All graphics magnify to full screen size to concisely present and reinforce these concepts. The Practice module provides the students, in a non-scored and non-graded environment, to practice skills acquired through studying. Engaging, interactive feedback prompts the student to right answers when wrong answers to questions are entered. The student has instant access to the study material for reference. In the Test module, the student takes a scored examination, the results of which are recorded in the A+LS Management System. Upon completion of the Test, the student electronically "turns in" the test and may instantly see test results and correct answers to questions missed. The Essay module allows the student to compose individual, free-form answers to a wide variety of questions and problems.
| LESSON # | LESSON TITLE | LESSON CONTENT |
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Roots and Radicals | Review of square roots and perfect squares and radicals; solving problems containing radicals; inverse of squaring numbers, irrational numbers, principal square roots |
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Real Number Properties 1 | Multiplication and division of radicals, simplifying radical expressions, radical exponents, irrational numbers, product property of rationals |
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Real Number Properties 2 | Addition and subtraction of radicals, like radicals and like terms, using the distributive property to solve problems |
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Rational Exponents | Using addition, subtraction, multiplication, and division and combinations of operations to solve problems with rational exponents |
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Equations | Identify radicals and solving equations with radicals |
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Imaginary Numbers | Identification and problem solving using imaginary numbers |
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Complex Numbers 1 | Solving addition and subtraction problems of complex pure and imaginary numbers |
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Complex Numbers 2 | Multiplication and division of complex numbers, using the commutative property to solve problems, the FOIL method of factoring and solving |
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Quadratic Equations 1 | Solving quadratic equations by completing the square, solving and factoring, completing the square to solve equations |
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Quadratic Equations 2 | Using the quadratic formula to solve problems, checking for reasonableness of all solutions |
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The Discriminant | Identifying and evaluating the discriminant of a quadratic equation; using the discriminant to determine the number of solutions to an equation |
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Roots | Equations involving the sum and products of roots and their connection to the coordinate plane |
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Quadratic Equations 3 | Rewriting equations in quadratic form to solve |
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Problem Solving | Solving problems using quadratic equations |
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Quadratic Relations | Identifying and illustrating distance and midpoint, solving problems with number lines, absolute value, the Pythagorean Theorem |
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Parabola | Characteristics and definition of parabola |
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Graphing Parabola | Plotting parabola on the coordinate plane |
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Circles | Circle characteristics; solving problems involving identification of circle parts and formulas |
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Ellipses | Characteristics of ellipses; plotting ellipses on the coordinate plane, identification and illustration of fixed points |
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Hyperbola | Characteristics of hyperbola, visual illustrations of hyperbola, intersection of planes and cones, identifying the difference between ellipses and hyperbola |
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Graphing Relations | Identifying relations; identifying functions; graphing quadratic relations and inequalities |
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Graphing Inequalities | Intersections of graphs of quadratic relations, graphing conic inequalities and intersections |
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Variations | Inverse and joint variations of linear functions; combined variation |
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Exponential Functions | Different strategies for simplifying and solving equations and expressions with rational positive and negative exponents |
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Inverse Functions | Ordered pairs, coordinates, the domain, identification and illustrations of the inverse function |
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Logarithmic Functions | Identification and explanation of logarithmic functions, the exponential/logarithmic scale, definition and examples of logarithms |
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Exponential Equations | Definition and examples of exponential equations, solving problems using the graphing calculator, properties of logarithms, significant digits, compound interest problems |
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Arithmetic Sequence | Definition and examples of arithmetic sequences, difference of numbers, finite sequences of numbers |
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Arithmetic Series | Definition and examples of arithmetic series in real world situations, identification of sigma, solving problems using arithmetic series |
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Geometric Sequence | Definition and examples of geometric sequence, geometric progression, terms of geometric sequences |
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Geometric Series | Definition and examples of geometric series, formulas for solving problems with geometric series |
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Infinite Geometric Series | Examples and definition of common ratios, formulas, convergent geometric series, solving problems with geometric series |
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Binomial Theorem | Identification of patterns and integral powers, finite series, coefficients, variable powers, factorials, solving factorial problems |
